Absence of Nonlocal Counter-terms in the Gauge Boson Propagator in Axial -type Gauges

TL;DR

This paper investigates the gauge boson two-point function in axial gauges using a novel exact path-integral approach, demonstrating the absence of nonlocal divergences and clarifying the relation to principal value prescriptions.

Contribution

It introduces an exact, Lorentz-compatible treatment of axial gauges that avoids nonlocal divergences and clarifies the connection to principal value prescriptions.

Findings

No nonlocal divergences in the two-point function.

The proper vertex differs from CPV only by finite terms.

The method simplifies calculations with a smooth light cone limit.

Abstract

We study the two-point function for the gauge boson in the axial-type gauges. We use the exact treatment of the axial gauges recently proposed that is intrinsically compatible with the Lorentz type gauges in the path-integral formulation and has been arrived at from this connection and which is a ``one-vector'' treatment. We find that in this treatment, we can evaluate the two-point functions without imposing any additional interpretation on the axial gauge 1/(n.q)^p-type poles. The calculations are as easy as the other treatments based on other known prescriptions. Unlike the ``uniform-prescription'' /L-M prescription, we note, here, the absence of any non-local divergences in the 2-point proper vertex. We correlate our calculation with that for the Cauchy Principal Value prescription and find from this comparison that the 2-point proper vertex differs from the CPV calculation only by finite terms. For simplicity of treatment, the divergences have been calculated here with n^2>0 and these have a smooth light cone limit.